Referring to portions of FIG. 1, in an artificial gas lift system (16), gas flows through a gas lift choke (4) and into an annulus (5). A gas injection valve (6) is placed at the deepest feasible point in a well. The gas injection valve is a check valve allowing the flow of gas only in one direction from an annulus (5) to a tubing (3), when the down-hole pressure in an annulus (5) is higher than in a tubing (3). This gas mixes with oil, which reduces the density of this mixture, so it results in the reduction of the well head. If a well is dead, it will start flowing as a result of the pressure differential between a reservoir (2) and the well head. As the head pressure become smaller, this create a pressure differential and the oil starts flowing upwards toward a production choke (7).
The biggest drawback in this system is the possibility of slug which is characterized by the intermittent type of gas flow, which can be also seen as instability of the gas lift system. Slug is the most detrimental effect to the performance of the control system, to oil production, and to the functionality of equipment.
The down-hole measurements are very difficult, however, and it would be very beneficial for the control purpose to have more accurate down-hole information. As a result, in some prior art systems state estimators are used to estimate the down-hole process variables from available measurements. A state estimator is an auxiliary dynamical system that provides estimates of process variables which are difficult or impossible to measure. There are quite a number of realizations of state estimators for a gas lift system that are available in literature. Aamo et al. (2005) proposed a nonlinear reduced-order observer for estimating the down-hole pressure, and combined it with a conventional proportional-integral (PI) controller. In the observer design, the states are taken as the masses of gas and liquid in the different volumes of the system. The mass of gas in the annulus is computed first from the measured surface pressures. For the estimation of the other two states, the pressure at the surface of both the annulus and the tubing are measured along with the flow through the production choke. Given the mass of gas in the annulus is a measured entity, the observer designed is dubbed a reduced-order observer, because it is not estimating all three states in the system.
Zhou et al. (2008) developed a nonlinear model for their system, which is an empirical model that qualitatively describes the behavior of the down-hole pressure, when there is severe slugging. A nonlinear observer in this case estimates the unmeasured down-hole states similar to Aamo et al. (2005). The controller in Zhou et al. (2008) is designed through an integrator back-stepping approach to eliminate the slugs in the fluctuating flow. In the proposed design, a parametrization for the states of the observer is required. The states of this model are taken as the down-hole pressure, its time derivative, and a variable proportional to the annulus-tubing differential pressure. The observer designed sees the down-hole pressure as the measured variable, and estimates the other two states accordingly. When pairing up the observer with a controller, Zhou et al. (2008) ensured global stability of the system along with transient performance. However, since this design depends on down-hole pressure measurements it is considered not feasible.
Jepsen et al. (2013) used a similar approach, where a simple nonlinear model is derived and verified by a laboratory setup. For this model an observer-based state feedback control is designed. The controller manipulates the opening of the production valve, based on pressure values returned and measured on the surface. In this case, the states are the masses of gas and liquid in the system. The presented laboratory setup includes a small scale 3 meters long PVC pipeline representing the tubing, a variable speed pump for the reservoir, and an air buffer tank connected to the tubing through a compressor to provide the required pressure. Comparing the simulation results from the nonlinear model developed with those from the experimental setup, the authors gave a benchmark for their work. Another control method developed by Jepsen et al. (2013) is for the nonlinear model, which is based on a linear observer. This is done through linearization of the original nonlinear model. In model linearization, an opening of the valve was taken at which both the measurements and the simulation results showed unstable behavior. This allows for the controlled system to reach stability in the most unstable regions of its operations. When designing the linear observer, the authors used the pole placement method. Jepsen et al. (2013) is one of the very few studies that consider the system from both a nonlinear and linear perspective.
Nikoofard et al. (2014) designed and compared different types of observers. The mathematical model designed was based on a lumped-parameter low-order model, where the states are the masses of gas and liquid in the different volumes. The first observer designed is a Lyapunov-based adaptive observer, which is a full-order observer for the states in the system; this is a conventional observer design method. The second observer designed is the Recursive Least Squares estimator. For this estimator the initial estimation error covariance is taken with large values; this leads to high correction vectors and therefore to a fast convergence of the states. Finally a Joint Unscented Kalman filter is introduced, using the Gaussian distribution; the filter estimates the average and covariance matrices for the estimation error with a few sample set points. When comparing these three methods, the authors noted that RLS has the best performance for parameter estimation while it has a lower measurement noise covariance. The adaptive observer has a better performance when it comes to parameter estimation while the measurement noise covariance is high.
Prior systems also include a real-time adaptive nonlinear observer for the estimation and control of an oil well hydrodynamic deep states by Govorkov et al. (2008), a fuzzy observer and controller in gas-lifted oil wells by Jahanshahi et al. (2008), and a high gain observer by Scibilia et al. (2008). Ali et al. (2015) provided a review on the applications of recent observers to chemical process systems and classified them into six classes.
U.S. Pat. No. 5,535,135 (1996) of Kevin J. Bush, et al. discloses a method and a system for measuring a chemical concentration of a gas exhausted from exhaust ports of a multi-cylinder internal combustion engine based on a Kalman-Bucy state estimator. The disclosed method and system claim compensation for the static and dynamic temporal and special effects characteristic of the multi-cylinder engine exhaust system and improvement of sensory response to rich and lean exhaust gases.
U.S. Pat. No. 5,845,627 (1998) of Peter M. Olin, et al. discloses a pneumatic state estimator for estimating gas flow and pressure at pneumatic nodes and flow branches within a reticulated engine system for engine control and diagnostic operations resolving net flow imbalances at specific pneumatic nodes and attributes.
U.S. Pat. No. 7,069,159 B2 (2006) of Marek Zima, et al. discloses a method, a computer program and a system for estimating a state of a large-scale electric power transmission network. The disclosed system claims that the invention can work completely independent of and redundant to existing SCADA systems.
U.S. Pat. No. 7,375,679 (2008) of Purusottam Mookerjee, et al. discloses a reduced state estimation with biased and out-of-sequence measurements from multiple sensors. The disclosure relates to the tracking of moving targets by multiple sensors, with different measurement bias for each sensor and feeding these measurements into a central processing site, possibly with different time delays. The disclosed process claims providing a computationally efficient recursive algorithm for optimally estimating the state of a system, using the criterion of minimizing the mean-square total error.
U.S. Pat. No. 7,908,112 B2 (2011) of Flavio Nardi, et al. discloses a system and method for estimating vehicle lateral velocity that defines a relationship between front and rear axle lateral forces and front and rear axle side-slip angles. The disclosed method claims providing an estimated vehicle lateral velocity using the selected virtual lateral velocity through the use of a closed loop Luenberger observer with a kinematic relationship between the lateral velocity and standard sensor measurements for lateral acceleration, yaw-rate and vehicle longitudinal velocity.
U.S. Pat. No. 8,700,279 B2 (2014) of R. A. Hansen, et al. discloses a method for optimizing a shift event in a vehicle which includes designating a clutch to be used as an oncoming clutch or an offgoing clutch in the shift event before executing the shift event, and processing a plurality of input values through a linear state observer to thereby determine, as an output value of the state observer, an estimated slip speed of the designated clutch. The disclosed method includes using a proportional-integral control module for the designated clutch to close the control loop on the estimated slip speed from the state observer, thereby smoothing a switching between state space equation in the state observer, and executing the shift event.
U.S. Pat. No. 8,706,333 B2 (2014) of Yonghua Li, discloses a method for controlling an electric vehicle including an internal combustion engine, a battery having a state of charge (SOC) and an open circuit voltage (OCV). The disclosed method includes establishing a system for estimating battery state of charge. The system includes an open circuit voltage estimation subsystem including an adaptive observer for estimating battery open circuit voltage based on a previous estimate of battery open circuit voltage.
U.S. Pat. No. 8,890,484 B2 (2014) of Xiaofeng Mao, et al. discloses a battery state of charge (SOC) estimator using a robust linear time invariant infinity observer, when connected to a plurality of loads.
U.S. Pat. No. 9,007,260 B2 (2015) of Yaron Martens, et al. discloses a method and apparatus for estimating and compensating for a broad class of non-Gaussian sensor and process noise. A coded filter combines a dynamic state estimator (for example, a Kalman filter) and a nonlinear estimator to provide approximations of the non-Gaussian process and sensor noise associated with a dynamic system. These approximations are used by the dynamic state estimator to correct sensor measurements or to alter the dynamic model governing evolution of the system state. The disclosed method and apparatus is used to estimate the position of a navigator. The coded filter leverages compressive sensing techniques in combination with error models based on concepts of compressibility and the application of efficient convex optimization processes.
U.S. Pat. No. 9,010,180 B2 (2015) of Simon Petrovic, et al. discloses a method and an observer for determining the exhaust manifold temperature in a turbocharged engine upstream of the turbine. The method comprises estimating a value of the exhaust manifold temperature based on a model, measuring a temperature downstream of the turbine, and correcting the value of the exhaust manifold temperature based on the measurement. The disclosed method claims enabling a sufficiently fast, accurate and robust determination of the exhaust manifold temperature with reduced effort and costs.
U.S. Pat. No. 9,097,798 B2 (2015) of Christopher J. Martens, et al. discloses a method and system for determining the position of a user device which can receive data signals from orbiting space vehicles. These data signals can be used for positioning calculation and/or track maintenance of the user device. The disclosed method and system relates to satellite navigation and estimating the position of fixed or moving user devices using an extended Kalman filter (EKF) state estimator for the track maintenance of the user device, based on tracking the changing positing of the user device.
U.S. Pat. No. 9,168,924 B2 (2015) of Jin-Woo Lee, et al. discloses a lane controller system installed on a host vehicle which may include components for self-diagnosing malfunctions on the vehicle. The disclosed system may include a vehicle state estimator for estimating the state of the vehicles. The disclosed system claims that the vehicle state estimator provides data to a path predicator for predicting the path that the vehicle is following, which is then used to correct the steering applied by the steering controller to the electrical power steering (EPS), or active front steering (AFS), or individual wheel brakes.
U.S. Pat. No. 9,222,237 B1 (2015) of Francisco R. Green, et al. discloses a weighted state estimator for controlling the position of an earthmoving equipment, which typically have a hydraulically controlled earthmoving implement, that can be manipulated by a joystick or other means in an operator control station of the machine. The implement state estimator generates an implement state estimate using Kalman filter that is based at least partially on (i) implement position signals from an implement angular rate sensor and an implement accelerometer, (ii) signals from the translational chassis movement indicator and the implement inclinometer, and (iii) one or more weighting factors representative of noise in the signals from the translational chassis movement indicator and the implement inclinometer.
U.S. Pat. No. 9,239,229 B2 (2016) of Stefan Xalter, et al. discloses a method and device for monitoring multiple mirror arrays in an illumination system of microlithographic projection exposure apparatus. The system also includes an instrument to provide a measurement signal, and a model-based state estimator configured to compute, for each element, an estimated state vector based on the measurement signal. The estimated state vector represents: a deviation of a light beam caused by the element; and a time derivative of the deviation. The disclosed system claims the suitability of using Kalman filter, the extended Kalman filter (EKF), the unscented Kalman filter (UKF) or the particle filter for state estimation.
U.S. Pat. No. 9,281,686 B2 (2016) of Jay P. Britton discloses a state estimation for cooperative electrical grids which is based on a local grid model and local electrical grid information. The local state estimation can reflect interactions and interconnections with other electrical grids by determining state estimation solution information based on the local grid model, local electrical grid information, and remote state estimator solution information associated with the other electrical grid. As such, a local state estimator can be configured to receive and employ remote state estimator solution information. This can be in addition to the model conventional technique or receiving a remote grid model and remote electrical grid information to estimate the conditions of the remote electrical grid. The disclosed method claims that state estimation solution information can be incremental to further reduce the amount of information to be transferred and the time needed to accomplish transmission of the information.